1. Field of the Invention
The present invention relates to a process control apparatus having at least a control loop for feedback-controlling a process controlled variable of a process to a set point by at least its proportional-integral or proportional-integral-derivative operation. More particularly, the present invention relates to a process control apparatus capable of automatically tuning the operating parameters and a method for adjustment of the operating parameters of a controller for use in a process control apparatus.
2. Description of the Prior Art
In the past, the tuning of PID control parameters in the PID controller of a process control apparatus is effected manually by the operator who is observing variations in control variables. This raises problems that the adjustment work becomes time-consuming and tuning results are differently affected by individuality of the operators.
On the other hand, a variety of systems based on control theory have been proposed wherein a setting test signal is applied to an object to be controlled so as to set a dynamic characteristics of the process and control parameters are turned to optimum values on the basis of setting results. In these proposals, however, it is expected that because of fluctuation of control variables due to the application of the setting test signal, quality is degraded or, particularly in a plant of high nonlinearity, abnormal states disadvantageously take place. Further, unless the setting test is performed each time the dynamic characteristics of the controllable object is changed, optimum values of operating parameters can not be obtained, thus leading to troublesome handling operations.
As described in "Expert Self-tuning Controller", Measurement Technology, pp 66-72, Nov., 1986, "PID-Self-Tuning Based on Expert Method" Measurement Technology, pp 52-59, Nov., 1986, JP-A-62-108306 and JP-A-61-245203, heuristic methods are also known wherein the tuning of control parameters is effected in consideration of the shape of responses of controlled variables.
Each of the above-described methods is arranged to modify the operating parameters in a predetermined relationship and based upon the overshoot amount for evaluating the controllability or the amplitude damping ratio by using the external values of the actual control response shape obtained by a detection. It is considered feasible for the above-described methods to involve a disadvantage in that, if the process controlled variable is disordered by noise, the external value of the actual control response shape is erroneously detected, causing the overshoot amount or the amplitude damping ratio to be obtained incorrectly. This leads to a problem that the operating parameters cannot be modified correctly.
A proposal relating to a PID controller having a function capable of tuning the PID operating parameter has been disclosed by the inventor of the present invention in Japanese Patent Laid-Open No. 63-247801. In accordance with the above-described PID controller, the control response waveform is observed, and an evaluating index computed from the result of the observation is used to tune the PID operating parameter in accordance with an adjustment rule corresponding to a plurality of control response waveforms and based upon fuzzy inference processing. According to the automatic tuning means of the above-described PID controller, the set point and the process controlled variable are arranged to be entered and only the set value or response waveform of the process controlled variable generated due to change in the disturbance is observed so as to tune the PID operating parameter.
However, the optimum value of the operating parameter tuned by observing the control response waveform generated due to change in the set point and the optimum value of the operating parameter tuned by observing the control response waveform generated due to the application of disturbance become different from each other. Therefore, according to the above-described PID controller, the tuning in a control loop in which change in the set point and application of disturbance exist together cannot sometimes be converged, resulting in the necessity of selecting a proper tuning.
However, the control response generates, due to change in the set point, an application of known disturbance and an interference from the other control loop (to be called "a unknown disturbance") in the case where a multi-variable process is the process to be controlled. Therefore, a multi-variable process control apparatus, having an automatic tuning means capable of stably converging the turning to a proper control response even when the above-described factors are mixed with one another, has been desired.
A method of adjusting the operating parameters of a controller of a process control apparatus has been disclosed in "Automatic Tuning System for a PID controller and based on Fuzzy Inference", 13-th System Symposium, Measurement Technology, Nov., 1987. The above-described method is arranged in such a manner that the feature quantity, such as overshoot amount E, damping ratio D, oscillation period ratio R or the like, are extracted from the response waveform of the process controlled variable at the time of step-changing the set point, and then operating parameters are determined from the thus obtained feature quantity on the basis of fuzzy inference. The fuzzy inference expresses the following adjustment rule about the qualitative expression in a fuzzy rule and determines operating parameters from the feature quantity by fuzzy operation using the fuzzy rule: "if the overshoot amount E and the damping ratio D are large, the proportion gain K.sub.p and the derivative time Tc.sub.1 are made small" (an example of the adjustment rule).
Hitherto, several tens of fuzzy rules have been needed in the conventional technology and the fuzzy rules, that is, the adjustment rules, must be constituted without involving any inconsistency. Therefore, a problem arises in that it takes too long a time to constitute the adjustment rules.
As a method of adjusting the operating parameters of a PID controller for a process control apparatus, there is available a partial model matching method as described in, for example, "Design Method for Control System Based on Partial Knowledge of Controllable Object", Transactions of the Society of Instrument and Control Engineers, Vol. 5, No. 4, pp 549/555, Aug., 1979.
The above-described partial model matching method is a method for determining the operating parameters of a PID controller so as to provide a closed loop transfer function W(s) of process controlled variable y(s) with respect to set point r (s) s: Laplacean partially coincide with the transfer function W.sub.r (s) of a reference model showing a satisfactory response. Then, a case in which a transfer function G.sub.p (s) of a process can be approximated by primary delay+dead time will now be considered. ##EQU1## where K: gain, T: time constant, L: dead time.
The transfer function G.sub.c (s) of the PID controller can be expressed by: ##EQU2##
The closed-loop transfer function W(s) of the process controlled variable y(s) with respect to the set point r(s) can be expressed as: ##EQU3##
Substitution of equations (1) and (2) into equation (3) gives ##EQU4##
Maclaurin's-expansion of the dead time transfer function e.sup.-LS gives ##EQU5##
On the other hand, the transfer function W.sub.r (s) of the reference model can be given from the following equation: ##EQU6## where .alpha..sub.i : coefficient, .sigma.: time scale factor.
In order to make the closed-loop transfer function W(s) of the process controlled variable y(s) with respect to the set point r(s) obtained by substituting equation (5) into equation (4) partially agree with the transfer function W(s) of the reference model expressed by equation (6), the following equation must be satisfied: ##EQU7##
The following equations (8) to (11) are obtained from equation (7) so that the operating parameters K.sub.p, T.sub.i and T.sub.d and the time scale factor .sigma. of the PID controller are determined. ##EQU8##
Since equation (11) is a cubic equation, complicated calculations are necessary to determine the minimum positive real root as the time scale factor .sigma. by solving the cubic equation. Therefore, a problem arises in that it takes too long a time to solve the above-described calculations by using a microcomputer. Therefore, a simple equation becomes necessary. As a result of the study of the results of calculations of minimum positive real roots of equation (11) about a variety of primary delay+dead time of a Kitamori model (.alpha..sub.2 =0.5, .alpha..sub.3 =0.15, .alpha..sub.4 =0.03 , . . . ), it has been found that the time scale factor .sigma. can be approximated as follows: EQU .sigma..apprxeq.1.37L (12).
However, a problem arises in that the approximate accuracy of equation (12) becomes unsatisfactory in a region in which the ratio L/T between the dead time L and the time constant T is small and in another region in which it is large.
Furthermore, according to the above-described conventional technology, the rise time of the control response cannot be adjusted.